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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Restrictions to continuous functions and Boolean algebras


Author: Ireneusz Recław
Journal: Proc. Amer. Math. Soc. 118 (1993), 791-796
MSC: Primary 26A21; Secondary 04A15, 06E99, 28A20, 54C30
MathSciNet review: 1152289
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Abstract: We show that every Borel function $ f:\mathbb{R} \to \mathbb{R}$ is continuous on a set $ A \notin \mathcal{J}$ if $ B(\mathbb{R})/\mathcal{J}$ is weakly distributive. We also show that CCC is not sufficient. We investigate some other conditions considering the problem of restrictions to continuous functions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1152289-8
PII: S 0002-9939(1993)1152289-8
Keywords: Continuity, weak distributivity, Boolean algebra, Lusin set
Article copyright: © Copyright 1993 American Mathematical Society